Struct graphene::Matrix

pub struct Matrix(_);

A structure capable of holding a 4x4 matrix.

The contents of the Matrix structure are private and should never be accessed directly.

Implementations

impl Matrix

pub fn decompose(&self) -> Option<(Vec3, Vec3, Quaternion, Vec3, Vec4)>

Decomposes a transformation matrix into its component transformations.

The algorithm for decomposing a matrix is taken from the CSS3 Transforms specification; specifically, the decomposition code is based on the equivalent code published in “Graphics Gems II”, edited by Jim Arvo, and available online.

Returns

true if the matrix could be decomposed

translate

the translation vector

scale

the scale vector

rotate

the rotation quaternion

shear

the shear vector

perspective

the perspective vector

pub fn determinant(&self) -> f32

Computes the determinant of the given matrix.

Returns

the value of the determinant

pub fn equal_fast(&self, b: &Matrix) -> bool

Checks whether the two given Matrix matrices are byte-by-byte equal.

While this function is faster than graphene_matrix_equal(), it can also return false negatives, so it should be used in conjuction with either graphene_matrix_equal() or near(). For instance:

⚠️ The following code is in C ⚠️

  if (graphene_matrix_equal_fast (a, b))
    {
      // matrices are definitely the same
    }
  else
    {
      if (graphene_matrix_equal (a, b))
        // matrices contain the same values within an epsilon of FLT_EPSILON
      else if (graphene_matrix_near (a, b, 0.0001))
        // matrices contain the same values within an epsilon of 0.0001
      else
        // matrices are not equal
    }

b

a Matrix

Returns

true if the matrices are equal. and false otherwise

pub fn row(&self, index_: u32) -> Vec4

Retrieves the given row vector at index_ inside a matrix.

index_

the index of the row vector, between 0 and 3

Returns

res

return location for the Vec4 that is used to store the row vector

pub fn value(&self, row: u32, col: u32) -> f32

Retrieves the value at the given row and col index.

row

the row index

col

the column index

Returns

the value at the given indices

pub fn x_scale(&self) -> f32

Retrieves the scaling factor on the X axis in self.

Returns

the value of the scaling factor

pub fn x_translation(&self) -> f32

Retrieves the translation component on the X axis from self.

Returns

the translation component

pub fn y_scale(&self) -> f32

Retrieves the scaling factor on the Y axis in self.

Returns

the value of the scaling factor

pub fn y_translation(&self) -> f32

Retrieves the translation component on the Y axis from self.

Returns

the translation component

pub fn z_scale(&self) -> f32

Retrieves the scaling factor on the Z axis in self.

Returns

the value of the scaling factor

pub fn z_translation(&self) -> f32

Retrieves the translation component on the Z axis from self.

Returns

the translation component

pub fn init_from_2d(
    &mut self,
    xx: f64,
    yx: f64,
    xy: f64,
    yy: f64,
    x_0: f64,
    y_0: f64
)

Initializes a Matrix from the values of an affine transformation matrix.

The arguments map to the following matrix layout:

⚠️ The following code is in plain ⚠️

  ⎛ xx  yx ⎞   ⎛  a   b  0 ⎞
  ⎜ xy  yy ⎟ = ⎜  c   d  0 ⎟
  ⎝ x0  y0 ⎠   ⎝ tx  ty  1 ⎠

This function can be used to convert between an affine matrix type from other libraries and a Matrix.

xx

the xx member

yx

the yx member

xy

the xy member

yy

the yy member

x_0

the x0 member

y_0

the y0 member

Returns

the initialized matrix

pub fn init_from_matrix(&mut self, src: &Matrix)

Initializes a Matrix using the values of the given matrix.

src

a Matrix

Returns

the initialized matrix

pub fn init_from_vec4(&mut self, v0: &Vec4, v1: &Vec4, v2: &Vec4, v3: &Vec4)

Initializes a Matrix with the given four row vectors.

v0

the first row vector

v1

the second row vector

v2

the third row vector

v3

the fourth row vector

Returns

the initialized matrix

pub fn init_frustum(
    &mut self,
    left: f32,
    right: f32,
    bottom: f32,
    top: f32,
    z_near: f32,
    z_far: f32
)

Initializes a Matrix compatible with Frustum.

See also: Frustum::init_from_matrix()

left

distance of the left clipping plane

right

distance of the right clipping plane

bottom

distance of the bottom clipping plane

top

distance of the top clipping plane

z_near

distance of the near clipping plane

z_far

distance of the far clipping plane

Returns

the initialized matrix

pub fn init_identity(&mut self)

Initializes a Matrix with the identity matrix.

Returns

the initialized matrix

pub fn init_look_at(&mut self, eye: &Vec3, center: &Vec3, up: &Vec3)

Initializes a Matrix so that it positions the “camera” at the given eye coordinates towards an object at the center coordinates. The top of the camera is aligned to the direction of the up vector.

Before the transform, the camera is assumed to be placed at the origin, looking towards the negative Z axis, with the top side of the camera facing in the direction of the Y axis and the right side in the direction of the X axis.

In theory, one could use self to transform a model of such a camera into world-space. However, it is more common to use the inverse of self to transform another object from world coordinates to the view coordinates of the camera. Typically you would then apply the camera projection transform to get from view to screen coordinates.

eye

the vector describing the position to look from

center

the vector describing the position to look at

up

the vector describing the world’s upward direction; usually, this is the Vec3::y_axis() vector

Returns

the initialized matrix

pub fn init_ortho(
    &mut self,
    left: f32,
    right: f32,
    top: f32,
    bottom: f32,
    z_near: f32,
    z_far: f32
)

Initializes a Matrix with an orthographic projection.

left

the left edge of the clipping plane

right

the right edge of the clipping plane

top

the top edge of the clipping plane

bottom

the bottom edge of the clipping plane

z_near

the distance of the near clipping plane

z_far

the distance of the far clipping plane

Returns

the initialized matrix

pub fn init_perspective(
    &mut self,
    fovy: f32,
    aspect: f32,
    z_near: f32,
    z_far: f32
)

Initializes a Matrix with a perspective projection.

fovy

the field of view angle, in degrees

aspect

the aspect value

z_near

the near Z plane

z_far

the far Z plane

Returns

the initialized matrix

pub fn init_rotate(&mut self, angle: f32, axis: &Vec3)

Initializes self to represent a rotation of angle degrees on the axis represented by the axis vector.

angle

the rotation angle, in degrees

axis

the axis vector as a Vec3

Returns

the initialized matrix

pub fn init_scale(&mut self, x: f32, y: f32, z: f32)

Initializes a Matrix with the given scaling factors.

x

the scale factor on the X axis

y

the scale factor on the Y axis

z

the scale factor on the Z axis

Returns

the initialized matrix

pub fn init_skew(&mut self, x_skew: f32, y_skew: f32)

Initializes a Matrix with a skew transformation with the given factors.

x_skew

skew factor, in radians, on the X axis

y_skew

skew factor, in radians, on the Y axis

Returns

the initialized matrix

pub fn init_translate(&mut self, p: &Point3D)

Initializes a Matrix with a translation to the given coordinates.

p

the translation coordinates

Returns

the initialized matrix

pub fn interpolate(&self, b: &Matrix, factor: f64) -> Matrix

Linearly interpolates the two given Matrix by interpolating the decomposed transformations separately.

If either matrix cannot be reduced to their transformations then the interpolation cannot be performed, and this function will return an identity matrix.

b

a Matrix

factor

the linear interpolation factor

Returns

res

return location for the interpolated matrix

pub fn inverse(&self) -> Option<Matrix>

Inverts the given matrix.

Returns

true if the matrix is invertible

res

return location for the inverse matrix

pub fn is_2d(&self) -> bool

Checks whether the given Matrix is compatible with an a 2D affine transformation matrix.

Returns

true if the matrix is compatible with an affine transformation matrix

pub fn is_backface_visible(&self) -> bool

Checks whether a Matrix has a visible back face.

Returns

true if the back face of the matrix is visible

pub fn is_identity(&self) -> bool

Checks whether the given Matrix is the identity matrix.

Returns

true if the matrix is the identity matrix

pub fn is_singular(&self) -> bool

Checks whether a matrix is singular.

Returns

true if the matrix is singular

pub fn multiply(&self, b: &Matrix) -> Matrix

Multiplies two Matrix.

Matrix multiplication is not commutative in general; the order of the factors matters. The product of this multiplication is (self × b)

b

a Matrix

Returns

res

return location for the matrix result

pub fn near(&self, b: &Matrix, epsilon: f32) -> bool

Compares the two given Matrix matrices and checks whether their values are within the given epsilon of each other.

b

a Matrix

epsilon

the threshold between the two matrices

Returns

true if the two matrices are near each other, and false otherwise

pub fn normalize(&self) -> Matrix

Normalizes the given Matrix.

Returns

res

return location for the normalized matrix

pub fn perspective(&self, depth: f32) -> Matrix

Applies a perspective of depth to the matrix.

depth

the depth of the perspective

Returns

res

return location for the perspective matrix

pub fn print(&self)

Prints the contents of a matrix to the standard error stream.

This function is only useful for debugging; there are no guarantees made on the format of the output.

pub fn project_point(&self, p: &Point) -> Point

Projects a Point using the matrix self.

p

a Point

Returns

res

return location for the projected point

pub fn project_rect(&self, r: &Rect) -> Quad

Projects all corners of a Rect using the given matrix.

See also: project_point()

r

a Rect

Returns

res

return location for the projected rectangle

pub fn project_rect_bounds(&self, r: &Rect) -> Rect

Projects a Rect using the given matrix.

The resulting rectangle is the axis aligned bounding rectangle capable of fully containing the projected rectangle.

r

a Rect

Returns

res

return location for the projected rectangle

pub fn rotate(&mut self, angle: f32, axis: &Vec3)

Adds a rotation transformation to self, using the given angle and axis vector.

This is the equivalent of calling init_rotate() and then multiplying the matrix self with the rotation matrix.

angle

the rotation angle, in degrees

axis

the rotation axis, as a Vec3

pub fn rotate_euler(&mut self, e: &Euler)

Adds a rotation transformation to self, using the given Euler.

e

a rotation described by a Euler

pub fn rotate_quaternion(&mut self, q: &Quaternion)

Adds a rotation transformation to self, using the given Quaternion.

This is the equivalent of calling Quaternion::to_matrix() and then multiplying self with the rotation matrix.

q

a rotation described by a Quaternion

pub fn rotate_x(&mut self, angle: f32)

Adds a rotation transformation around the X axis to self, using the given angle.

See also: rotate()

angle

the rotation angle, in degrees

pub fn rotate_y(&mut self, angle: f32)

Adds a rotation transformation around the Y axis to self, using the given angle.

See also: rotate()

angle

the rotation angle, in degrees

pub fn rotate_z(&mut self, angle: f32)

Adds a rotation transformation around the Z axis to self, using the given angle.

See also: rotate()

angle

the rotation angle, in degrees

pub fn scale(&mut self, factor_x: f32, factor_y: f32, factor_z: f32)

Adds a scaling transformation to self, using the three given factors.

This is the equivalent of calling init_scale() and then multiplying the matrix self with the scale matrix.

factor_x

scaling factor on the X axis

factor_y

scaling factor on the Y axis

factor_z

scaling factor on the Z axis

pub fn skew_xy(&mut self, factor: f32)

Adds a skew of factor on the X and Y axis to the given matrix.

factor

skew factor

pub fn skew_xz(&mut self, factor: f32)

Adds a skew of factor on the X and Z axis to the given matrix.

factor

skew factor

pub fn skew_yz(&mut self, factor: f32)

Adds a skew of factor on the Y and Z axis to the given matrix.

factor

skew factor

pub fn to_2d(&self) -> Option<(f64, f64, f64, f64, f64, f64)>

Converts a Matrix to an affine transformation matrix, if the given matrix is compatible.

The returned values have the following layout:

⚠️ The following code is in plain ⚠️

  ⎛ xx  yx ⎞   ⎛  a   b  0 ⎞
  ⎜ xy  yy ⎟ = ⎜  c   d  0 ⎟
  ⎝ x0  y0 ⎠   ⎝ tx  ty  1 ⎠

This function can be used to convert between a Matrix and an affine matrix type from other libraries.

Returns

true if the matrix is compatible with an affine transformation matrix

xx

return location for the xx member

yx

return location for the yx member

xy

return location for the xy member

yy

return location for the yy member

x_0

return location for the x0 member

y_0

return location for the y0 member

pub fn transform_bounds(&self, r: &Rect) -> Rect

Transforms each corner of a Rect using the given matrix self.

The result is the axis aligned bounding rectangle containing the coplanar quadrilateral.

See also: transform_point()

r

a Rect

Returns

res

return location for the bounds of the transformed rectangle

pub fn transform_box(&self, b: &Box) -> Box

Transforms the vertices of a Box using the given matrix self.

The result is the axis aligned bounding box containing the transformed vertices.

b

a Box

Returns

res

return location for the bounds of the transformed box

pub fn transform_point(&self, p: &Point) -> Point

Transforms the given Point using the matrix self.

Unlike transform_vec3(), this function will take into account the fourth row vector of the Matrix when computing the dot product of each row vector of the matrix.

See also: graphene_simd4x4f_point3_mul()

p

a Point

Returns

res

return location for the transformed Point

pub fn transform_point3d(&self, p: &Point3D) -> Point3D

Transforms the given Point3D using the matrix self.

Unlike transform_vec3(), this function will take into account the fourth row vector of the Matrix when computing the dot product of each row vector of the matrix.

See also: graphene_simd4x4f_point3_mul()

p

a Point3D

Returns

res

return location for the result

pub fn transform_ray(&self, r: &Ray) -> Ray

Transform a Ray using the given matrix self.

r

a Ray

Returns

res

return location for the transformed ray

pub fn transform_rect(&self, r: &Rect) -> Quad

Transforms each corner of a Rect using the given matrix self.

The result is a coplanar quadrilateral.

See also: transform_point()

r

a Rect

Returns

res

return location for the transformed quad

pub fn transform_sphere(&self, s: &Sphere) -> Sphere

Transforms a Sphere using the given matrix self. The result is the bounding sphere containing the transformed sphere.

s

a Sphere

Returns

res

return location for the bounds of the transformed sphere

pub fn transform_vec3(&self, v: &Vec3) -> Vec3

Transforms the given Vec3 using the matrix self.

This function will multiply the X, Y, and Z row vectors of the matrix self with the corresponding components of the vector v. The W row vector will be ignored.

See also: graphene_simd4x4f_vec3_mul()

v

a Vec3

Returns

res

return location for a Vec3

pub fn transform_vec4(&self, v: &Vec4) -> Vec4

Transforms the given Vec4 using the matrix self.

See also: graphene_simd4x4f_vec4_mul()

v

a Vec4

Returns

res

return location for a Vec4

pub fn translate(&mut self, pos: &Point3D)

Adds a translation transformation to self using the coordinates of the given Point3D.

This is the equivalent of calling init_translate() and then multiplying self with the translation matrix.

pos

a Point3D

pub fn transpose(&self) -> Matrix

Transposes the given matrix.

Returns

res

return location for the transposed matrix

pub fn unproject_point3d(&self, modelview: &Matrix, point: &Point3D) -> Point3D

Unprojects the given point using the self matrix and a modelview matrix.

modelview

a Matrix for the modelview matrix; this is the inverse of the modelview used when projecting the point

point

a Point3D with the coordinates of the point

Returns

res

return location for the unprojected point

pub fn untransform_bounds(&self, r: &Rect, bounds: &Rect) -> Rect

Undoes the transformation on the corners of a Rect using the given matrix, within the given axis aligned rectangular bounds.

r

a Rect

bounds

the bounds of the transformation

Returns

res

return location for the untransformed rectangle

pub fn untransform_point(&self, p: &Point, bounds: &Rect) -> Option<Point>

Undoes the transformation of a Point using the given matrix, within the given axis aligned rectangular bounds.

p

a Point

bounds

the bounds of the transformation

Returns

true if the point was successfully untransformed

res

return location for the untransformed point

impl Matrix

pub fn init_from_float(&mut self, v: &[f32; 16])

Initializes a Matrix with the given array of floating point values.

v

an array of at least 16 floating point values

Returns

the initialized matrix

pub fn from_2d(xx: f64, yx: f64, xy: f64, yy: f64, x_0: f64, y_0: f64) -> Matrix

pub fn from_float(v: &[f32; 16]) -> Matrix

pub fn from_matrix(src: &Matrix) -> Matrix

pub fn from_vec4(v0: &Vec4, v1: &Vec4, v2: &Vec4, v3: &Vec4) -> Matrix

pub fn new_frustum(
    left: f32,
    right: f32,
    bottom: f32,
    top: f32,
    z_near: f32,
    z_far: f32
) -> Matrix

pub fn new_identity() -> Matrix

pub fn new_look_at(eye: &Vec3, center: &Vec3, up: &Vec3) -> Matrix

pub fn new_ortho(
    left: f32,
    right: f32,
    top: f32,
    bottom: f32,
    z_near: f32,
    z_far: f32
) -> Matrix

pub fn new_perspective(
    fovy: f32,
    aspect: f32,
    z_near: f32,
    z_far: f32
) -> Matrix

pub fn new_rotate(angle: f32, axis: &Vec3) -> Matrix

pub fn new_scale(x: f32, y: f32, z: f32) -> Matrix

pub fn new_skew(x_skew: f32, y_skew: f32) -> Matrix

pub fn new_translate(p: &Point3D) -> Matrix

pub fn to_float(&self) -> [f32; 16]

Converts a Matrix to an array of floating point values.

Returns

v

return location for an array of floating point values. The array must be capable of holding at least 16 values.

Trait Implementations

impl Clone for Matrix

fn clone(&self) -> Matrix

Returns a copy of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Matrix

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Hash for Matrix

fn hash<__H: Hasher>(&self, state: &mut __H)

Feeds this value into the given Hasher.

fn hash_slice<H>(data: &[Self], state: &mut H) where
    H: Hasher, 

Feeds a slice of this type into the given Hasher.

impl Ord for Matrix

fn cmp(&self, other: &Matrix) -> Ordering

This method returns an Ordering between self and other.

fn max(self, other: Self) -> Self

Compares and returns the maximum of two values.

fn min(self, other: Self) -> Self

Compares and returns the minimum of two values.

fn clamp(self, min: Self, max: Self) -> Self

Restrict a value to a certain interval.

impl PartialEq<Matrix> for Matrix

fn eq(&self, other: &Self) -> bool

This method tests for self and other values to be equal, and is used by ==.

fn ne(&self, other: &Rhs) -> bool

This method tests for !=.

impl PartialOrd<Matrix> for Matrix

fn partial_cmp(&self, other: &Matrix) -> Option<Ordering>

This method returns an ordering between self and other values if one exists.

fn lt(&self, other: &Rhs) -> bool

This method tests less than (for self and other) and is used by the < operator.

fn le(&self, other: &Rhs) -> bool

This method tests less than or equal to (for self and other) and is used by the <= operator.

fn gt(&self, other: &Rhs) -> bool

This method tests greater than (for self and other) and is used by the > operator.

fn ge(&self, other: &Rhs) -> bool

This method tests greater than or equal to (for self and other) and is used by the >= operator.

impl StaticType for Matrix

fn static_type() -> Type

Returns the type identifier of Self.

impl Eq for Matrix